Cairo -LRB- CNN -RRB- -- Egypt 's prime minister appealed for calm and asked protesters to return to their homes Tuesday following four days of violence in Cairo and a day after the nation 's Cabinet offered to resign .

`` We have met the demands of the people and submitted our resignations , '' Prime Minister Essam Sharaf said , according to Egypt 's Nile TV . `` Now please put the interests of the country first . ''

Fresh violence broke out Tuesday near the city 's Tahrir Square . For several hours , protesters hurled stones at police and chanted , calling for the downfall of the Supreme Council of Armed Forces . The military-led government began leading the country after protesters ousted President Hosni Mubarak in February .

Demonstrators apparently tried to defend Tahrir Square as they faced off with police on a connecting street . The square was once a hub for the movement that led to Mubarak 's ouster and is now a center for the protests against Egypt 's military rulers .

Egyptian police responded with tear gas and rubber bullets , forcing protesters to retreat briefly before they returned with renewed intensity . Violence also spread to other parts of Egypt .

Field Marshal Mohamed Hussein Tantawi , head of Egypt 's Supreme Council of the Armed Forces , will address the nation Tuesday , according to Egyptian state broadcaster Al Masriya . The latest report contradicted an earlier one saying he would speak `` shortly . ''

After Mubarak 's fall , military leaders took control with the promise that eventually a civilian government would be elected and take over .

Military leaders still say they will hand over power to a new government when one is elected . However , while parliamentary elections are set to take place Monday , a complex electoral process follows , and the presidential vote could be a year away .

Demonstrators say they are concerned the military , which would continue to be Egypt 's top authority until a president is in place , wants to keep a grip on the country . Many also have voiced anger about a proposed constitutional principle that would shield the military 's budget from scrutiny by civilian powers . They say they worry the military would become a state within a state .

On the streets of Cairo , some protesters have gone further , shouting that they believe Mubarak is running the military council and , in fact , the entire country from prison . He and his sons Gamal and Alaa face charges of corruption and of killing protesters .

Three Americans were arrested Monday outside the Interior Ministry in Cairo . Authorities accuse them of throwing Molotov cocktails , said Adel Saeed , a spokesman for the office of Egypt 's general prosecutor .

The young men are students at American University in Cairo , according to university spokeswoman Morgan Roth . She identified them as Gregory Porter , 19 , of Glenside , Pennsylvania ; Luke Gates , 21 , of Bloomington , Indiana ; and Derrik Sweeney , 19 , from Jefferson City , Missouri .

Porter attends Drexel University in Pennsylvania , Gates goes to Indiana University and Sweeney studies at Georgetown University , she said . At least two of them were on a semesterlong study abroad program in Cairo .

David Lynfield , deputy press officer in the U.S. Embassy in Cairo , said the `` claims are being currently investigated . '' The university is working with the embassy , Roth said .

Tuesday 's violence marks the fourth day of clashes between security forces and protesters . Twenty-nine protesters have died in the clashes since Saturday , said Hisham Sheeha , spokesman for Egypt 's Health Ministry . About 1,785 people have been injured , he said .

Earlier , Dr. Adil al-Adawi , another ministry spokesman , said about 200 of those injuries came Monday .

Egypt 's Interior Ministry said 102 officers and conscripts have been injured , with wounds ranging from gunshots to burns from Molotov cocktails . One officer was shot in the head .

Some political factions have vowed to hold a sit-in Tuesday at Tahrir Square , demanding the immediate resignation of the Supreme Council . They also demand the immediate punishment of those who have killed protesters in the past few days .

The Alliance of the Revolutionaries of Egypt is calling the event a `` million man sit-in . ''

The Muslim Brotherhood , one of the largest organizations in the nation , has said that its members will not join that protest .

`` We did n't start this mess , '' said engineering student Mahmour Radwan , who traveled to Cairo from Alexandria on Tuesday with two friends to join the protests . He said authorities started it , when they killed people `` and put them in the street . ''

Radwan and many other protesters were equipped with surgical masks and other items in an attempt to protect themselves from the clouds of tear gas . Young women stood nearby , holding bottles of water and poised to treat those overcome by the tear gas .

Violence also spread to Alexandria ahead of a planned `` million man '' protest there . One person was killed and 60 others injured in that city , said al-Adawi , a Health Ministry spokesman . Thousands of people clashed with police Monday night near the city 's police headquarters . Rocks were thrown and tear gas used , said activist Huda Al-Sadani . Some people were arrested , Al-Sadani said , and clashes continued throughout the night .

Two of the deaths came in the city of Ismalia , said Sheeha , a Health Ministry spokesman . Violence also was reported in the city of Suez .

Amid the unrest , Egypt 's Cabinet offered to resign Monday night . Justice Minister Mohamed Abdelaziz al-Juindy explained that this move to quit the government was driven by opposition to the security forces ' crackdown on demonstrators .

`` I resigned because of the events in Tahrir -LRB- Square -RRB- , because of the political responsibility , '' al-Juindy said .

The Supreme Council has not said whether the resignations were accepted .

As the potential political shuffling played out , animosity and violence continued to simmer in the streets .

Saeed , the spokesman for the general prosecutor 's office , said 127 demonstrators who had been arrested in Cairo since Saturday have been released . Another five have been `` detained temporarily for further investigation . ''

The military council has said on its Facebook page it is `` extremely sorry for what the events have led to . '' And spokesman Maj. Mohamed Askar said late Monday that the Supreme Council has ordered a fact-finding mission to assess what has happened .

Moreover , the Supreme Council also is calling upon `` all political forces to hold dialogue as soon as possible in order to address the escalation '' of unrest , Askar said .

However , Amnesty International , in a report issued this month , said the Supreme Council , `` in the name of ensuring security and stability ... -LRB- has -RRB- committed numerous human rights violations , ignoring the very demands for social justice and fundamental freedoms that triggered the uprising . ''

'' ... Since assuming power in February , the Supreme Council of the Armed Forces has repeatedly pledged to break the cycle of repression entrenched over the past 30 years . In reality , however , it has resorted to familiar patterns of abuse . ''

A recent endorsement in full of Egypt 's emergency law and its expansion , after it was restricted last year under Mubarak , is considered the largest example of human rights violation , the organization said . However , it alleged demonstrations have been violently dispersed and protesters have been arrested , detained and tortured `` before being tried unfairly before military courts and convicted . ''

In addition , Amnesty International alleged , the Supreme Council has placed arbitrary restrictions on the media . Some television stations have been raided and ordered closed , while satellite television stations have been frozen . The council has also failed to address discrimination of women , according to the group .

`` If the hopes of the uprising are to be realized , urgent action is needed now to ensure that one repressive rule is not simply replaced with another , '' the report said .

CNN 's Ivan Watson and Michael Pearson and journalist Mohamed Fadel Fahmy contributed to this report .

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NEW : Three arrested American students identified

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Report : Prime minister appeals for calm , asks protesters to return home

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Official : Twenty-nine people have been killed since Saturday , 1,785 injured

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Some political factions plan a `` million man sit-in '' on Tuesday